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hal-00719016, version 1

Waiting time asymptotics in the single server queue with service in random order

Onno Boxma 1, 2, Serguei Foss () 3, Jean-Marc Lasgouttes () 4, Rudesindo Núñez Queija 2

Queueing Systems 46, 1 (2004) 35-74

Abstract: We consider the single server queue with service in random order. For a large class of heavy-tailed service time distributions, we determine the asymptotic behavior of the waiting time distribution. For the special case of Poisson arrivals and regularly varying service time distribution with index −ν, it is shown that the waiting time distribution is also regularly varying, with index 1 − ν, and the pre-factor is determined explicitly. Another contribution of the paper is the heavy-traffic analysis of the waiting time distribution in the M/G/1 case. We consider not only the case of finite service time variance, but also the case of regularly varying service time distribution with infinite variance.

  • 1:  Department of Mathematics and Computer Science
  • Eindhoven University of Technology – Technishe Universiteit Eihdhoven
  • 2:  Centrum voor Wiskunde en Informatica (CWI)
  • Netherlands Organisation for Scientific Research – CWI
  • 3:  Department of Actuarial Mathematics and Statistics [Edinburgh]
  • Heriot-Watt University
  • 4:  PREVAL (INRIA Rocquencourt)
  • INRIA
  • Domain : Mathematics/Probability
  • Comment : single server queue – service in random order – heavy-tailed distribution – waiting time asymptotics – heavy-traffic limit theorem
 
  • hal-00719016, version 1
  • http://hal.inria.fr/hal-00719016
  • oai:hal.inria.fr:hal-00719016
  • From: Jean-Marc Lasgouttes <>
  • Submitted on: Wednesday, 18 July 2012 17:07:55
  • Updated on: Friday, 24 August 2012 15:06:30